1. Field of the Invention
This invention relates generally to the measurement of distance by means of an electromagnetic field and more particularly to the measurement of distance by means of a component of a vector potential magnetic field A for which the CURL A=0.
2. Description of the Prior Art
It is known in the prior art to provide a distance measurement system by generating an electromagnetic radiation field from a transmitter and measuring the time for the radiation field to reach the target object and return to a receiver. Because electromagnetic radiation travels with the speed of light, the time between transmission of the radiation and the detection of the reflected radiation by the receiver, (the receiver having a known spatial relationship with the transmitter) defines the distance. Familiar examples include microwave band ranging and optical (i.e., laser) reflection techniques. This technique for measuring distance is limited by the opacity of the intervening media to the transmitted electromagnetic radiation.
The Maxwell equations, which govern the prior art distance measuring techniques by electromagnetic fields can be written: ##EQU1## where E is the electric field density, H is the magnetic field intensity, B is the magnetic flux density, D is the electric displacement, J is the current density and .rho. is the change density. In this notation the bar over a quantity indicates that this is a vector quantity, i.e., a quantity for which a spatial orientation is required for complete specification. The terms CURL and DIV refer to the CURL and DIVERGENCE mathematical operations and are denoted symbolically by the .gradient..times. and .gradient..multidot. mathematical operators respectively. Furthermore, the magnetic field intensity and the magnetic flux density are related by the equations B=.omega.H, while the electric field density and the electric displacement are related by the equation D=.epsilon.H. These equations can be used to describe the transmission of electromagnetic radiation through a vacuum or through various media.
It is known in the prior art that solutions to Maxwell's equations can be obtained through the use of electric scalar potential functions and magnetic vector potential functions. The electric scalar potential is given by the expression: ##EQU2## where .phi.(1) is the scalar potential at point 1, .rho.(2) is the charge density at point 2, r.sub.12 is the distance between point 1 and 2, and the integral is taken over all differential volumes dv(2). The magnetic vector potential is given by the expression: ##EQU3## where A(1) is the vector potential at point 1, .epsilon..sub.o is the permittivity of free space, C is the velocity of light, J(2) is the (vector) current density at point 2, r.sub.12 is the distance between point 1 and point 2 and the integral is taken over all differential volumes. The potential functions are related to Maxwell's equations in the following manner: ##EQU4## where GRAD is the GRADIENT mathematical operation and is denoted by the .gradient. mathematical operator. EQU B=CURL A 8.
where A can contain, for completeness, a term which is the gradient of a scalar function. In the remaining discussion, the scalar function and the electric scalar field will be taken to be substantially zero. Therefore, attention will be focused on the magnetic vector potential A.
In the prior art literature, consideration has been given to the physical significance of the magnetic vector potential field A. The magnetic vector potential field was, in some instances, believed to be a mathematical artifice, useful in solving problems, but devoid of independent physical significance.
More recently, however, the magnetic vector potential has been shown to be a quantity of independent physical significance. For example, in quantum mechanics, the Schroedinger equation for a (non-relativistic, spinless) particle with charge g and mass m moving in an electromagnetic field is given by ##EQU5## where h is Plank's constant divided by 2.pi., i is the imaginary number .sqroot.-1, .phi. is the electric scalar potential experienced by the particle, A is the magnetic scalar potential experienced by the particle and .psi. is the wave function of the particle. The ability of quantum mechanical systems to be influenced by the magnetic vector potential field has resulted in devices which can be used to detect the magnetic vector potential field.